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C2×C5×(C127⋊C3)⋊C7 #40998673

order26670
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×(C127⋊C3)⋊C7
unambiguous semidirect product(C2×C127⋊C3)⋊(C5×C7)
unambiguous semidirect product(C2×C127⋊C7)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C127⋊C3)⋊C7
unambiguous semidirect product(C2×C5×C127⋊C7)⋊C3

Splittings

Fitting, socle, HallC2×C5×C127 ⋊ C3×C7
derived, SylowC127 ⋊ C2×C3×C5×C7
HallC2×C5×C127⋊C7 ⋊ C3
HallC5×C127⋊C7 ⋊ C2×C3
HallC2×C5×C127⋊C3 ⋊ C7
HallC5×C127⋊C3 ⋊ C2×C7
HallC2×C127⋊C7 ⋊ C3×C5
HallC127⋊C7 ⋊ C2×C3×C5
HallC2×C127⋊C3 ⋊ C5×C7
HallC5×C127 ⋊ C2×C3×C7
HallC127⋊C3 ⋊ C2×C5×C7
HallC2×C127 ⋊ C3×C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C5(C127⋊C3)⋊C7
commutator, cosocle, hypocenterC127C2×C3×C5×C7
FrattiniC1G
Fitting, socleC2×C5×C127C3×C7
LCSG ▷ C127
UCSC1 ◁ C2×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1270

Conjugacy classes & character table

270 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26670, 7);